Introduction to Judgment Aggregation

(EASSS: European Agent Systems Summer School 2018)




Judgment aggregation is a field in social choice theory and mathematical economics that studies the procedures, such as the majority rule, for aggregating sets of logical propositions. In the last ten odd years, judgment aggregation became an important support in AI, knowledge representation, and multiagent systems, as it provides a general theory for modelling situations where a central mechanism is designed to reconcile possibly conflicting Knowledge Bases, Ontologies, plans, or sets of constraints.

The focus of this tutorial is to provide the reader with a map of results of judgment aggregation for a number of logical frameworks that are used in applications to AI, multiagent systems, and knowledge representation. We start by presenting the framework of judgment aggregation. Then, we present the main results of judgment aggregation for classical propositional logic (e.g. possibility theorems, agenda characterization). Then, we extend the treatment of judgment aggregation to other logics. Firstly, we discuss a number of extensions of classical propositional logics; in particular, the family of Description Logics and a number of modal logics. Secondly, we focus on logical systems that are weaker than classical logics (non-classical logics).

A number of tutorial related to judgment aggregation recently presented at the major AI venues (e.g. ESSLLI, AAMAS, IJCAI). This tutorial is dedicated to highlighting the logical aspects of the theory of aggregation.


Topics covered:

  1. Basics of judgment aggregation.
  2. List and Pettit’s main theorem, agenda properties, and characterisation results.
  3. Judgment aggregation in extensions of propositional logics (Description Logics, Modal logics).
  4. Judgment aggregation for ontology aggregation.
  5. Judgment aggregation in non-classical logics.